Reduction of order, resummation, and radiation reaction

The Landau-Lifshitz equation is the first in an infinite series of approximations to Lorentz-Abraham-Dirac obtained from `reduction order'. We show that this divergent, predicting wildly different dynamics at successive perturbative orders. Iterating reduction order ad infinitum a constant crossed field, we obtain motion which free erratic behaviour perturbation theory. Borel-Pad\'e resummation divergent accurately reproduces equation, using as little two coefficients. Comparing with our results for large times optimal truncation typically amounts but fails capture resummed over short times.